On Families of Numerical Semigroups with two Coprime Generators and Dimension three

TL;DR

This paper explores properties of numerical semigroups with two coprime generators in three dimensions, revisiting algorithms for pseudo-Frobenius numbers and introducing a family of n-dimensional semigroups with bounded type.

Contribution

It provides a new perspective on known facts for low-dimensional numerical semigroups and introduces a family of n-dimensional semigroups with specific properties.

Findings

Re-investigation of algorithms for pseudo-Frobenius numbers.

Introduction of a family of n-dimensional numerical semigroups.

Analysis of semigroups with at most three generators and coprimality.

Abstract

This paper examines in a new way some known facts about numerical semigroups especially when the number of minimal generators (that is the embedding dimension) is at most three and at least two minimal generators are coprime. For such semigroups, an algorithm is re-investigated to find the pseudo-Frobenius numbers. A certain family of $n$ dimensional numerical semigroups of type at most $n-1$ is also given.